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Pairs of diagonal quartic forms: the non-singular Hasse principle

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Joerg Bruedern, Trevor D. Wooley

Number Theory · Submitted 8 Oct 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables.

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arXiv ID2110.04349 (version 1)
Pith ID7BFZDY72, Pith's permanent record of this paper and its review
CitationJoerg Bruedern, Trevor D. Wooley. "Pairs of diagonal quartic forms: the non-singular Hasse principle." arXiv:2110.04349 (2021). https://pith.science/paper/7BFZDY72
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,594 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.38 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables. result 0.81 0.96 0.95 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables.

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1 arXiv paper cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

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Papers citing it · 7 sentences without a confident label

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  • Hence, by orthogonality, one has [equation] The methods of [ref] rest on this and closely related identities, choosing $h(α)=|g(α)|^u$ with suitable quartic Weyl sums $g$ and a positive real number $u$.

    Pairs of diagonal quartic forms: the asymptotic formulae · Introduction · 0.98

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